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Journal of Physical Studies 11(4), 473–480 (2007)
DOI: https://doi.org/10.30970/jps.11.473 THE DEVELOPMENT OF SPHERICALLY SYMMETRICAL PERTURBATION IN COSMOLOGICAL MODELS WITH DARK ENERGY. AN APPROXIMATION OF THE IDEAL LIQUIDYu. Kulinich1, B. Novosyadlyj1, V. Pelykh2
1Ivan Franko National University of Lviv, Astronomical
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The development of spherically symmetrical perturbation was considered within the framework of cosmological models with dark energy on the basis of ideal liquid approximation. To reach the generality dark energy is represented as generalized component governed by state equation $p_{(g)}\equiv p_{(g)}(ρ_{(g)},S)$, where $S$ is entropy, and barionic component is included into a dust-like component with the state equation $p_{(d)}=0$. For such two-component medium the system of equations was built to describe the development of spherically symmetrical inhomogeneity with an arbitrary profile of radial density distribution at the non-linear stage of its evolution. These equations have been thoroughly analized. It was shown that cosmological models with a generalized component with state equation $p_{(g)}= -ρ_{Λ}$ at $ρ_{(g)}^0>ρ_{Λ}$ are equivalent to the $Λ$CDM models with proper values of parameters. Thus the result from [Yu. Kulinich, B. Novosyadlyj, J. Phys. Stud. {\bf 7}, 234 (2003); E. L. Lokas, Y. Hoffman, in ıt Proceedings of the 3rd International Workshop on the Identification of Dark Matter}, edited by N. J. C. Spooner, V. Kudryavtsev (World Scientific, Singapore, 2001), p. 121] where parameters of collapse were determined for the $Λ$CDM-models are still valid for a wider class of models. In the models with non-zero velocity of acoustical oscillations in the generalized component $c_{s(g)}^2\ne 0$, the development of central regions depends on the profile, and consequently on its dimensions. Besides, if $c_{s(g)}^2<0$ then perturbations of the generalized component appear to be very unstable to fragmentation which contradicts a small anisotropy of the cosmic microwave background. If condition $c_{s(g)}^2>0$ is valid then perturbations of the generalized component with the scale smaller than $R_g\equiv c_{s(g)}H_0^{-1}$ stop their development due to dissipation. Therefore the scales of perturbation of the generalized component appears to be constrained from below by the scale of $R_g$.
PACS number(s): 98.80.Ik, 95.36.+x, 95.35.+d